Examining Measurement Invariance in Bayesian Item Response Theory Models: A Simulation Study
Journal of Measurement and Evaluation in Education and Psychology, vol.14, no.1, pp.19-32, 2023 (ESCI, Scopus, TRDizin)
- Publication Type: Article / Article
- Volume: 14 Issue: 1
- Publication Date: 2023
- Doi Number: 10.21031/epod.1101457
- Journal Name: Journal of Measurement and Evaluation in Education and Psychology
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
- Page Numbers: pp.19-32
- Keywords: bayes factor, bayesian IRT models, Measurement invariance, random item effects modelling
- Akdeniz University Affiliated: Yes
Abstract
The aim of the study is to determine a measurement invariance cut-off point based on item parameter differences in Bayesian Item Response Theory Models. Within this scope, the Bayes factor is estimated for testing measurement invariance. For this purpose, a simulation study is conducted. The data were generated in the R software for each simulation condition under the one-parameter logistic model for 10 binary (1-0 scored) items. The invariance test was performed for various group sizes (n=500, 1000, 1500 and 2000) and difficulty parameters (dk=0, dk=0.1, dk=0.3, dk=0.5 and dk=0.7). The Bayesian analyzes were performed on the WINBUGS using the codes written in the R. A Bayes factor that provides evidence for measurement invariance was calculated depending on the parameter differences. The Savage-Dickey density ratio, one of the MCMC sampling schemas, was used to calculate the Bayes factor. As a result, if the item parameter difference is dk=0.3 and group sizes are 1500 or larger, the measurement invariance cannot be achieved. However, for small sample sizes (n=1000 or less) measurement invariance interpretation should be done carefully. When the dk=0.5, there are invariant items only in n=500. According to Bayes factor test results, evidence has been produced when dk=0.7 that measurement invariance cannot be achieved.